Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}7x+7y &= 7 \\ x+2y &= -8\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $2y = -x-8$ Divide both sides by $2$ to isolate $y$ $y = {-\dfrac{1}{2}x - 4}$ Substitute this expression for $y$ in the first equation. $7x+7({-\dfrac{1}{2}x - 4}) = 7$ $7x - \dfrac{7}{2}x - 28 = 7$ Simplify by combining terms, then solve for $x$ $\dfrac{7}{2}x - 28 = 7$ $\dfrac{7}{2}x = 35$ $x = 10$ Substitute $10$ for $x$ back into the top equation. $7( 10)+7y = 7$ $70+7y = 7$ $7y = -63$ $y = -9$ The solution is $\enspace x = 10, \enspace y = -9$.